Question

9. In a certain school, of the students had over 80%

in math. If 465 students had 80% or less, how many
had over 80%?

Answer 1

Let's use algebra to solve the problem. Let x be the total number of students in the school. Then, we know that the number of students who had over 80% in math is 0.6x (since 60% is the same as 0.6 as a decimal). We also know that 465 students had 80% or less in math, so the number of students who had over 80% in math is x - 465. Setting these two expressions equal to each other, we get:

0.6x = x - 465

Solving for x, we get:

0.4x = 465

x = 465 / 0.4

x = 1162.5

Since the number of students must be a whole number, we round up to the nearest whole number to get:

x = 1163

Therefore, the number of students who had over 80% in math is:

0.6x = 0.6 * 1163 = 698.

Answer 2

4 students

Explanation:

Let's call the total number of students in the school "x". We know that a certain percentage of them had over 80% in math, and the rest (100% - that percentage) had 80% or less.

Let's call the percentage of students who had over 80% "p". Then, we can set up the following equation:

p% of x + (100% - p%) of x = x

We can simplify this to:

p/100 * x + (100 - p)/100 * x = x

Multiplying both sides by 100 to get rid of the denominators, we get:

px + (100 - p)x = 100x

Simplifying further:

px + 100x - px = 100x

100x = 465

x = 465/100 = 4.65 (rounded to two decimal places)

So the total number of students in the school is approximately 4.65. However, we can't have a fraction of a student, so let's round up to the nearest whole number and assume there are 5 students in the school.

Now we can use the information given to find the number of students who had over 80%:

"of the students had over 80% in math"

implies that

p% of x = number of students who had over 80%

So if we plug in the values we have:

p% of 5 = number of students who had over 80%

Simplifying:

0.01p * 5 = number of students who had over 80%

0.05p = number of students who had over 80%

We don't know the value of p, but we can solve for the number of students who had over 80% for different values of p. For example:

If p = 90, then:

0.05(90) = 4.5

So 4.5 students had over 80%. Since we can't have half a student, we can assume that 4 students had over 80%.

Alternatively, we can solve for p using the information given:

"of the students had over 80% in math"

implies that

p% of x = number of students who had over 80%

So:

p% of x = number of students who had over 80%

p% of 5 = number of students who had over 80%

0.01p * 5 = number of students who had over 80%

0.05p = number of students who had over 80%

We know that the number of students who had over 80% is some integer value between 0 and 5, inclusive. We can test different values of p within this range to see if they give us an integer solution:

If p = 90, then:

0.05(90) = 4.5

This is not an integer solution, so p = 90 is not the correct answer.

If p = 80, then:

0.05(80) = 4

This is an integer solution, so p = 80 is the correct answer. Therefore, 4 students had over 80%.